The invention is directed to a method and apparatus for measuring the circularity and mean radius of nominally cylindrical and/or tapered objects.
For large submersible vessels which are subject to extreme pressures, it is extremely important that the cross sectional configuration of the hull be as nearly circular as possible to minimize any possible abberations or weak points or regions in the surface of the hull which could produce a collapse under pressure.
Several prior art systems have been developed to measure circularity. One such systems entails the taking of a plurality of measurements of internal radii to locate the true center of the supposedly circular hull. The measured radii then are processed through a least mean squares fit program to create a circle that locates a center which enables one to determine the best fit circle. This then determines if the cross sectional circularity of the vessel hull is or is not within tolerance. The problem with this technique is that it must be carried out when the hull is initially fabricated and completely empty, i.e., without internal bulkheads, equipment, etc., that might impede the taking of radii measurements. Thus, if subsequent distortions are caused during vessel construction, the likelihood is that they may go undetected, at least by this technique.
Another prior art technique entails the positioning of a "true cylinder" around the vessel hull being measured. Measurements of circularity are made based on this "true cylinder". Here, the "true cylinder" sometimes undergoes distortion due to sagging, thereby causing inaccurate readings.
Still another prior art technique is based on photogrammetry. External markings are placed along a path defined by the intersection of a plane which is perpendicular to the vessel axis and which intersects the circumference on the vessel hull. A plurality of overlaping photographs are then taken along the aforesaid path and based on these photographs the distance between markings is determined and a calculation is made of the true circularity of the hull. The problem with this technique is that it requires an externally unobstructed view of the hull surface. Thus scaffoldings and other construction equipment must be cleared away, at considerable cost and inconvenience to the shipbuilder.
The present invention overcomes these prior art problems by providing a measurement gauge and method of measurement that is more accurate than prior art techniques and that may be employed at any stage of the vessel's construction, without regard to internal obstructions.
Broadly the invention comprises a method for determining the shape of a surface wherein the surface is divided into a plurality of contiguous segments with the junction of adjacent segments defining stations. A reference plane is established which plane is perpendicular to a reference axis. The plane extends through the surface and the intersection of the plane with the surface defines the shape of the path which is to be measured. The curvature of each station is measured and the closure property of the surface is invoked. Subsequently, a deviation of each of the stations from the nominal shape of interest is determined.
In one aspect of the invention, the measurement of the shape of the surface includes digitizing the general curvature equation ##EQU1## to determine the deviations from the nominal shape of interest. In another aspect of the broad scope of the invention, the shape of the surface of interest is determined by using the perturbation theory about the nominal shape and then digitizing the result to determine the deviations from the nominal shape of interest.
The preferred embodiment of the invention includes determining the circularity of a curved surface surrounding a reference axis. A reference plane through a vessel is established which plane is perpendicular to the reference axis and which plane extends through the surface the intersection of the plane with the surface defining a curved path. The path is divided into a plurality of equal length contiguous segments with the junction of the adjacent segments defining stations. The deviation b.sub.i of each station is measured from a chord which extends between the preceeding and succeeding stations adjacent to the station. The curvature at each station is calculated and the closure property of the surface is invoked. The deviation of each of the stations from the best fit circle and the mean radius of the surface which is the radius of the best fit circle are determined.
The apparatus broadly comprises a gauge and a data collection station. The gauge includes a rigid frame having two mutually spaced support legs. The legs have hardened tapered feet and are separated by the nominal chord size between alternate stations. A gauge indicator is located at a point midway between the measurement feet. The gauge indicator measures the deviation (b.sub.i) of the hull surface from a chord connecting the measurement feet. Preferably an offset steadying leg is secured adjacent to one of the support legs to provide a three point mount for the indicator gauge on the cylinder. An automatic data collector is used to accept data from the gauge indicator.
The data collection station basically comprises a CPU station which accepts the gauge data automatically or manually, processes the data and outputs the data.
The method and apparatus are also used for determining the circularity of tapered objects (having sloping surfaces) where the surface containing the closed curved path is not parallel to the reference axis but is at an angle to the reference axis. A correction factor is applied to the deviation measurements, b.sub.i, to provide a value of b.sub.i that would be obtained if the measurement were made in the plane normal to the reference axis. The gauge is modified to include a second indicator offset from the first indicator. Both indicators are used to determine the slope between stations i and i-1.
In another aspect of the preferred embodiment the determination of the mean radius is made by a technique which produces more accurate results then can be achieved with prior art techniques. Although this technique is used in the preferred embodiment it may also be used with other prior art techniques for the determination of deviations from the best fit circle.